[M-GI29] Computational sciences on the universe, galaxies, stars, planets and their environments

[MGI29-03] A high-order transport scheme on the cubed sphere using radial basis functions

*Koji Ogasawara¹, Takeshi Enomoto² (1.Graduate school of science, Kyouto University, 2.Disaster prevention research institute, Kyoto university)

Keywords:dynamical core, cubed sphere, radial basis function, meshless method

Radial Basis Function (RBF) yields a meshless and high-order method for hyperbolic partial differential equations (PDE). In geofluid dynamics, The RBF method has been adapted for solving the shallow water equations (Flyer and Wright 2009) and mantle convection (Wright et al. 2010). The RBF-generated Finite Difference (RBF-FD) is suitable for large scale simulations such as shallow water equations (Tillenius et al. 2015) and global electric circuit model (Bayona et al. 2015). Recently, the saturation error (RBF-FD fails to converge with increasing resolution) can be avoided easily by adding polynomials to the interpolation matrix (Flyer et al, 2016: FET16). For solving the transport equation on the sphere using FET2016, two schemes have been reported (Gunderman et al. 2020, Shankar et al. 2018).These schemes are based on 3D cartesian coordinates, which is more inefficient than the formulation in a 2D coordinates for solving PDE on the sphere.
To address this problem, we apply the cubed sphere to the transport equation on the sphere using FET16. In this study, we investigate the accuracy using a solid body rotation test case. The model is advanced in time using the classical fourth-order Runge Kutta method with the fourth-order hyperviscosity. The maximum determinant nodes and icosahedral grid are used with a stencil size of 55.
The result show that new scheme achieves sixth-order convergence. The new scheme does not saturate under 40 km resolution. When the test tracer passes through the corner, the normalized maximum error does not grow to cause a spike.